



The
measure of the distance all of the way around a circle



is equal
to the diameter times pi. 





That
means the measure of the distance 


half the
way around the circle 


is equal
to the diameter times pi divided by 2. 











One
fourth of the way around the circle would be ... 











Since all
of the way around the circle is 360 degrees 


and one
fourth of the way around the circle is 90 degrees 


we can
write that last one as: 











Great!
What's the big deal about that? 





The big
deal is this. 


As long
as we only want to know stuff like the length of 


half way
around or a quarter of the way around the circle 


we don't
have much problem. 


But what
of we want to know the length of a piece of circle 


that
makes an angle of 42 degrees at the center. 


Like this
... 











To find
the length that we need: 











With this
trick, we can find the length 


of any
piece of any circle. 





Example: 


Find the
length of a piece of circle 


that
makes an angle of 35 degrees at the center. 


The
radius of the circle is 6. 





Since the
radius of the circle is 6, 


the
diameter is 2 x 6 = 12. 











copyright 2005 Bruce Kirkpatrick 
